Theorems · Definition · category theory
CategoryTheory.Projective.factorThru
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{P X E : C} → [CategoryTheory.Projective P] → (P ⟶ X) → (e : E ⟶ X) → [CategoryTheory.Epi e] → P ⟶ EAn arbitrarily chosen factorisation of a morphism out of a projective object through an epimorphism.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.Projectivestatement and proof · cited by 78
- CategoryTheory.Projective.factorsproof · cited by 6
Cited by14
Results whose statement or proof uses this declaration.
- CategoryTheory.Projective.factorThru_compstatement · cited by 8
- CategoryTheory.ShortComplex.Exact.liftFromProjective_compproof · cited by 5
- CompHaus.liftproof · cited by 3
- CategoryTheory.ShortComplex.Exact.liftFromProjectiveproof · cited by 3
- Profinite.liftproof · cited by 3
- CategoryTheory.Projective.factorThru_comp_assocstatement and proof · cited by 2
- CategoryTheory.ProjectiveResolution.liftFZeroproof · cited by 1
- CategoryTheory.Projective.hasLiftingProperty_of_isZeroproof · cited by 1
- CochainComplex.isSplitEpi_to_singleFunctor_obj_of_projectiveproof · cited by 1
- CategoryTheory.regularTopology.isSheafFor_regular_of_projectiveproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.splittingOfProjectiveproof · cited by 0